A survey conducted in the wake of the prime minister's long-awaited speech on Wednesday showed a five-point Conservative jump on last month - mostly at the expense of the UK Independence Party - almost halving Labour's lead to six.
Cameron insists he wants to stay in the EU but pledged to renegotiate the relationship to claw back powers and offer voters a choice of that deal or exit by the end of 2017 if the Conservatives are returned to power in 2015.
His pledge came amid intense pressure from eurosceptic backbenchers concerned about the threat posed by a resurgent Ukip but has been attacked by Labour and his Liberal Democrat coalition partners.
Ukip, which has registered significant advances in recent months, fell back four points to 10%.
The poll found a majority of voters backed Labour and Lib Dem warnings that Cameron's position would cause "years of uncertainty which will be bad for the British economy" by 43% t0 30%.
But a majority also now believe that leaving the EU would in itself be bad for the economy in terms of lost jobs and trade - by 38% to 36%, a turnaround from November when 40% disagreed and 36% agreed.
There was also a significant shift in the numbers saying the UK should quit Brussels regardless of whether powers could be returned, voters disagreeing by 43% to 33% - the exact opposite of the previous poll.
However the change in the numbers expecting to vote "yes" if powers were returned rose only slightly.
Cameron enjoys the confidence of 42% of voters that he is "good at standing up for Britain's interests in the European Union" while only 22% said they believed Miliband would be if he became prime minister.
And though the Tory leader still has an overall negative personal rating as premier - by 32% to 46% - it has significantly improved since the 27% to 51% gap of last month and is his best since June 2011.
The poll was released as Miliband - who has said the party is not in favour of the referendum promised by the prime minister - faced renewed calls from within his own party for an immediate in/out referendum.
But in an interview with the Sunday Times, the Labour leader was confident about his decision.
He said: "I just don't think it's in the national interest.
"Right now it doesn't make sense to commit to a referendum years ahead."
He added that he believes the prime minister is putting his party ahead of the country by offering an EU referendum.
"Has he changed his mind because he's changed his view about the national economic interest? Or has he changed his mind because there's pressure in the Conservative party and he's worried about UKIP?
"I contend it's the second, not the first. That's why I've stuck to the positioning we've always had," Miliband said.
On Radio 4 on Saturday, both shadow Foreign Secretary Danny Alexander and Shadow Welsh Secretary Peter Hain said they backed Miliband's view that it was the wrong timescale for a referendum.
Former Europe minister Keith Vaz, a supporter of EU membership, said it was "time to settle the question of Britain's membership in the EU once and for all".
"I support a referendum because, like David Cameron, Ed Miliband and Nick Clegg, I believe the future of our country is in Europe. I am supportive, but pragmatic about the European project," he wrote in the Sunday Mirror.
"I accept British people rightly feel the EU is not delivering on its promises. Reform is necessary. We need better, stronger and earlier scrutiny by Parliament of EU measures.
"However, the proposed timescale is wrong.
"A four-year wait is destabilising for our country, but also for what we are hoping to achieve in Britain's interest in the EU. It sends the wrong message to the rest of the world at a time of global financial crisis.
"The PM cannot allow the European Question to overshadow the critical issues that will confront our economy over the next few years. The time for a referendum is now. The people must decide. Let's do it!"
Labour former prime minister Tony Blair used an article in the Mail on Sunday to issue a rallying cry to the "sensible, solid majority" in favour of membership to start campaigning hard to make the case for a "yes" vote.
The UK leaving the EU would be an "extraordinary denial of its own interests", he wrote, accusing Mr Cameron of alienating potential European allies by opening the door to exit for party political gain.
"We don't know what the rest of Europe will decide. The referendum won't happen for four or five years. The only certain
thing is the uncertainty.
"That is why Ukip is rejoicing and it really doesn't matter what David Cameron comes back with by way of a deal. It will never be enough for them.
"They're like the old Left in the Labour Party or the new Right in the fringe parties of Europe and the Tea Party in the US.
They have a perfect right to make their point. But they shouldn't decide the policy of a serious nation."
He warned that Britain spent 20 years trying to get into Europe after Winston Churchill "didn't feel the need for Britain to be part of it.
"It is important not to repeat that pattern. I believe there is a sensible, solid majority in the UK for us to stay in Europe. It is time to start mobilising it."Suggest a correction